A robustified Newton based extremum seeking for engine optimization

Großbichler, Martin; Schmied, Roman; Polterauer, Philipp; Waschl, Harald; Re, Luigi del

doi:10.1109/acc.2016.7525423

Cited by 7 publications

(4 citation statements)

References 15 publications

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“…We are now going to apply the fundamental theorem of calculus, together with some mathematical tools, to show that the right hand-side of ( 21) may be expressed in function of the Lie-brackets of the vector fields, plus a remainder. We will then show that the remainder may be bounded so as to obtain (10).…”

Section: Appendix C Proof Of Lemmamentioning

confidence: 99%

Extremum Seeking with Intermittent Measurements: A Lie-brackets Approach

Labar¹,

Ebenbauer²,

Marconi³

2022

Preprint

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Extremum seeking systems are powerful methods able to steer the input of a (dynamical) cost function towards an optimizer, without any prior knowledge of the cost function. To achieve their objective, they typically combine time-periodic signals with the on-line measurement of the cost. However, in some practical applications, the cost can only be measured during some regular time-intervals, and not continuously, contravening the classical extremum seeking framework. In this paper, we first analyze how existing Lie-bracket based extremum seeking systems behave when being fed with intermittent measurements, instead of continuous ones. We then propose two modifications of those schemes to improve both the convergence time and the steady-state accuracy in presence of intermittent measurements. The performances of the different schemes are compared on a case study.

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Section: Appendix C Proof Of Lemmamentioning

confidence: 99%

Extremum Seeking with Intermittent Measurements: A Lie-brackets Approach

Labar¹,

Ebenbauer²,

Marconi³

2022

Preprint

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show abstract

“…Compared with the off-line model-based calibration, the amount of test data for online modeling is reduced, but it is difficult to guarantee the model accuracy. However, model-based online calibration takes the engine as a black box and obtains the control parameters' combination through iterative optimization 11,12 on the test bench. Besides, response surface methodology is a common way for engine modeling.…”

Section: Introductionmentioning

confidence: 99%

“…The most common non-model-based online calibration algorithm is extremum seeking (ES), including newton-based extremum seeking (NB-ES) and gradient-based extremum seeking (GB-ES). Großbichler et al 11 calibrated diesel engine injection parameters based on NB-ES. Since there is no guarantee that the Hessian matrix used in NB-ES is reversible, the global optimal results may not be found.…”

Section: Introductionmentioning

confidence: 99%

Study on momentum gradient descent on-line engine calibration algorithm combined with search space division

Huang,

Wang,

2023

International Journal of Engine Research

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Because of the control problem complexity, engine calibration becomes a multi-object nonconvex optimization problem (MONCOP). To solve this problem and shorten the calibration time, this study proposes an innovative on-line engine calibration algorithm which combines momentum gradient descent algorithm with search space division (MGD-SSD). Firstly, taking a two-stroke kerosene engine as the research object, the engine response model is built by support vector machine (SVM), and based on the analysis of the spark timing and air-to-fuel ratio calibration problem, MAPs of objective function value under three typical engine operation conditions are established. Then the design of MGD-SSD is introduced in detail. The search space division is used to find the appropriate initial point quickly and the momentum gradient descent algorithm is used to quickly find the global best point through the appropriate initial point. A comparative study on three methods including genetic algorithm (GA), genetic and gradient descent hybrid algorithm (GGD) and MGD-SSD is carried out through benchmark function test and virtual calibration test. All tests show that the MGD-SSD is able to find the global optimal solution with higher accuracy and fewer iterations. Finally, the bench test of MGD is carried out, and the validity of the algorithm is verified.

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“…For spark igni-tion engines, spark timing has been adjusted using ES, see Mohammadi et al (2014) and Hellström et al (2013). For Diesel engines, in Großbichler et al (2016) the fuel injection profile is adjusted, while in Lewander et al (2012) the reference signal for closed-loop controlled CA 50 is adjusted. In most cases a BSFC equivalent cost function is optimized.…”

Section: Introductionmentioning

confidence: 99%